Solids with icosahedral symmetry

Main article: Icosahedral symmetry

## Contents

* 1 Solids with full icosahedral symmetry
* 1.1 Platonic solids
* 1.2 Achiral Archimedean solids
* 1.3 Achiral Catalan solids
* 1.4 Kepler-Poinsot solids
* 1.5 Achiral nonconvex uniform polyhedra
* 2 Chiral Archimedean and Catalan solids
* 3 Chiral nonconvex uniform polyhedra
* 4 See also

## Solids with full icosahedral symmetry

Platonic solids \- regular polyhedra (all faces of the same type)

{5,3}  |
{3,5}

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Archimedean solids \- polyhedra with more than one polygon face type.

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3.10.10  | 50px
4.6.10  | 50px
5.6.6  | 50px
3.4.5.4  | 50px
3.5.3.5

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Catalan solids \- duals of the Archimedean solids.

50px
V3.10.10  | 50px
V4.6.10  | 50px
V5.6.6  | 50px
V3.4.5.4  |
V3.5.3.5

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### Platonic solids

Name  | Picture  | Faces  | Edges  | Vertices  | Edges per face  | Faces meeting
at each vertex

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dodecahedron |

(Animation)

| 12 | 30 | 20 | 5 | 3
icosahedron | Icosahedron

(Animation)

| 20 | 30 | 12 | 3 | 5

### Achiral Archimedean solids

Name  | picture  | Faces  | Edges  | Vertices  | Vertex configuration

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icosidodecahedron
(quasi-regular: vertex- and edge-uniform)  | Icosidodecahedron
(Video) | 32 | 20 triangles
12 pentagons | 60 | 30  | 3,5,3,5
truncated dodecahedron | Truncated dodecahedron
(Video) | 32 | 20 triangles
12 decagons | 90  | 60  | 3,10,10
truncated icosahedron
or commonly football (soccer ball)  | Truncated icosahedron
(Video) | 32 | 12 pentagons
20 hexagons | 90  | 60  | 5,6,6
rhombicosidodecahedron
or small rhombicosidodecahedron  | Rhombicosidodecahedron
(Video) | 62 | 20 triangles
30 squares
12 pentagons  | 120 | 60 | 3,4,5,4
truncated icosidodecahedron
or great rhombicosidodecahedron  | Truncated icosidodecahedron
(Video) | 62 | 30 squares
20 hexagons
12 decagons  | 180 | 120 | 4,6,10

### Achiral Catalan solids

Name  | picture  | Dual Archimedean solid  | Faces  | Edges  | Vertices  | Face Polygon

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rhombic triacontahedron
(quasi-regular dual: face- and edge-uniform)  | Rhombic triacontahedron
(Video) | icosidodecahedron | 30  | 60  | 32  | rhombus
triakis icosahedron | Triakis icosahedron
(Video) | truncated dodecahedron | 60  | 90  | 32  | isosceles triangle
pentakis dodecahedron | Pentakis dodecahedron
(Video) | truncated icosahedron | 60  | 90  | 32  | isosceles triangle
deltoidal hexecontahedron | Deltoidal hexecontahedron
(Video) | rhombicosidodecahedron | 60  | 120  | 62  | kite
disdyakis triacontahedron
or hexakis icosahedron  | Disdyakis triacontahedron
(Video) | truncated icosidodecahedron | 120  | 180  | 62  | scalene triangle

### Kepler-Poinsot solids

### Achiral nonconvex uniform polyhedra

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## Chiral Archimedean and Catalan solids

Archimedean solids:

Name  | picture  | Faces  | Edges  | Vertices  | Vertex configuration

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snub dodecahedron
or snub icosidodecahedron (2 chiral forms)  | Snub dodecahedron (Ccw)
(Video)
50px|Snub dodecahedron (Cw)
(Video) | 92 | 80 triangles
12 pentagons | 150  | 60  | 3,3,3,3,5

Catalan solids:

Name  | picture  | Dual Archimedean solid  | Faces  | Edges  | Vertices  | Face Polygon

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pentagonal hexecontahedron | Pentagonal hexecontahedron (Ccw)50px|Pentagonal hexecontahedron (Cw)
(Video)(Video) | snub dodecahedron | 60  | 50  | 92  | irregular pentagon

## Chiral nonconvex uniform polyhedra

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## See also

* The Fifty Nine Icosahedra

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